In the remainder part, just like in decimals, we can cut the remaining whole number into 10 smaller parts-giving us x/10. With this we simply put a zero after the remainder. Also, from where we first “cut” the whole number into 10 smaller pieces, we can place a decimal point. In my case double vertical line for easy reminder. As we cut the number into smaller pieces by 10, we can continue until we reach the end or a repeating pattern (also into infinitely small values).

Also when the divisor is with a decimal point, we can just simply move the decimal place of the dividend equal to the number of decimal moves until the divisor looks like a whole number.

You are correct in saying that this method doesn’t emphasize thinking about place value. However, does the standard algorithm really require thinking about place value? Most kids don’t even realize that they are working with place value. Asking “How many times does 12 go into 48?” pays no attention to whether that is 4800 or .048. It is only when students are asked to understand more deeply why the algorithm works that they focus on place value.

This method does not simplify using the long division algorithm and is less for working with multi-digit problems, so as Shelley says, it is a great intro to help kids break down the long division algorithm before learning it. I would add that this structure could also be used to teach polynomial division, as each term could go in its own distinct box.

I couldn’t disagree more. This method is 💯 rooted in place value. Each digit is in its own place value box. You could put all the zeroes in there (expanded form) for explaining purposes but then get them out to simplify the process. I substitute the numbers in the boxes with place value blocks on day 2 or 3 so they can see how this method is based on place value. It works well for showing why you regroup the leftover value as you move to the right. Don’t knock something until you try it and evaluate it thoroughly. This method is wonderful and there’s no reason to learn the standard way. This IS the standard way with a little extra organization.

How many hundred times will 2 go into 300? We say how many hundred because this is the number we are going to write in the hundreds place. We can say how many times does 2 go into 3, and then multiply that by 100. It will go in 1 hundred times. We’ll write a 1 in the hundreds place.

100×2 is 200, so we’re going to subtract a 2 in the hundreds place. That’s the part we’ve already used. So now we have 1 hundred left. We’ll bring that 100 into the tens place. So now in the tens, we have 120 which we’re calling 12 tens. In the tens place, how many times can 2 go into 12 tens? 6 times. Since that’s in the tens place, it means 60, and 2 x 60 is 120.

And so on. My son’s really solid on place value and the meaning of each digit, so this explanation worked beautifully for him, and was much easier to visualize than if I’d used the same teaching style with the traditional method. It’s also more efficient to write, and leaves less room for copying or place value errors than partial quotient. It also lends itself much more easily to decimals than does partial quotient. All this is important because he is dysgraphic. The less he needs to write and line up, the better.

I am trying to learn this method to better learn how to help my daughter who is learning this method in school.
@J Riley i figured out a way to do this method with multi-digit divisors i will try to explain without the use of actual boxes. (lets assume each line is a new box each R will move into next box as normal)
12/6725=?
12 / 67 = 5 R7
12 / 72 = 6 R0
12 / 05 = 0 R5 (at this point we have a remainder of 5)
so our answer is 560 R5
lets try a 3 digit divisor
120 / 64925 = ?
120 /649 = 5 R49
120 / 492 = 4 R12
120 / 125 = 1 R5
so our answer is 541 R5
as you can see from the examples for 2 digit divisors, divide first into the first 2 digits (if it will go , if not read further).
For 3 digit divisors divide first into the first 3 digits ( if it will go , if not read further)
now lets try an example where you can’t follow these steps
34 /12465 = ?
34 / 124 = 3 R22
34 / 226 = 6 R22
34 / 225 = 6 R21
so our answer is 366 R21
all you do is divide first into the first 3 digits
remember each line is a different box in the box method so how i recommend teaching this with multi-digit divisors is instead of creating multiple boxes at the start create a new box each time you need one.
Maybe Shelley Gray could create an example on the website that reflects this? but in the meantime just use the above examples try on a piece of paper recreating my examples in boxes ( remember each line is a new box).
I know without a graphic “box” it maybe hard to visualize but try it out its the same principle just where you start whether you divide into the first digit or the first 2 digits etc.
I hope this helps 🙂

I like to show my students a variety of methods for dividing. Sometimes, you can teach them with conceptual understanding of place value time and time again, and they still don’t get it. I NEVER think teaching a different method, after you introduce using conceptual understanding, is a bad thing. You might actually have students who finally get it, and that is always a good thing.

One question: Does this method work with a divisor larger than one digit? The video only demo’d one-digit divisors.

Hi Vickie! Yes, you are correct in saying that this method does not use place value understanding. In the beginning of the blog post, that’s why I mentioned that this is NOT a mental math based approach, but can be used for those who are planning on teaching traditional long division (which also does not rely on place value understanding). I also address this in the video, but I’ll try to edit this post to make it more clear. I absolutely agree with you that teaching for understanding is vitally important. In this blog post I also link to posts on the partial quotients and box methods, which are much more mental math focused.